Whereas a bit, the basic unit of digital electronics, always has the value 0 or 1 because of binary logic, a quantum bit, the basic unit of quantum calculation, may be a random combination, i.e. a superposition of the values 0 and 1. The mathematic expression of the state of a quantum bit is a|0>+b|1>, in which a and b are complex numbers meeting the equation |a|2+|b|2=1 and in which the quantum states |0> and |1> correspond to the values 0 and 1 of an ordinary bit.
So far, no real quantum computer has been conceived or constructed, although research is being done in this domain from the aspects of different disciplines. The rapidly increasing interest in recent years is explained by a desire to achieve a revolution in digital data processing. A computer operating on the conventional principle utilises fixed feed data, whereas a quantum computer employs the superposition principle of quantum mechanics, enabling it to calculate different combinations of all possible feed data by one single operation different in parallel computation. This enables a quantum computer to perform laborious calculations, which would be impossible for ordinary computers having ever so high speed. Such calculations include factor division of a high number, involving the problem of data protection in modern society, and simulation of quantum mechanical systems, which opens vertiginous perspectives in the study of the genesis of life and the origin of diseases, for instance.
The computing steps are followed by a measurement of the quantum state of quantum bits. In the measurement process, the quantum state of the quantum bit collapses according to quantum mechanic principles from the superposition state a|0>+b|1> either to the basic state |0> or the basic state |1>. The prime application of this invention is its potential of rapid and accurate measurement of quantum bits of a certain type. Measurement of the state of quantum bits in superconducting nano-structures has proved at least equally difficult as their use for computing operations.
In a superconductor, the electrons appear as so-called Cooper pairs, which are loosely bound coherent electron pairs, i.e. pairs vibrating at the same rate. The supercurrent of a Cooper pair passes without energy losses, and this is essential in maintaining the coherence of a quantum bit. A superconducting current may additionally penetrate through an insulation having a thickness of about 1-2 nanometres owing to the tunnelling phenomenon of quantum mechanics. Such a structure is called a tunnel junction. The energy of a tunnelling supercurrent is described by the term Josephson energy EJ, which is the higher, the stronger the tunnelling current. If a Cooper pair is brought to a superconductor island of the size of approx. one micrometer, the accomplished work, which is described by the term Cooper pair charging energy ECP, may be greater than the energy of the thermal vibrations at a sufficiently low temperature. At temperatures clearly below one Kelvin, which are obtained by straightforward cooling methods, such as eluting coolers, ECP and EJ are the highest energies and hence phenomena relating to these are predominant in physical processes.
A phase-quantum bit is a superconducting quantum bit. A supercurrent induced in a current loop made of superconducting material proceeds in the loop in principle over any distance. The basic states |0> and |1> of a phase-quantum bit are associated with the direction of the current circulating in the superconducting loop containing tunnel junctions. A phase-quantum bit is generally characterised by the condition ECP<<EJ. The phase Φ over a circuit component is defined as the time integral of the voltage V with the equation:
                    ϕ        =                                            2              ⁢              e                        ℏ                    ⁢                                    ∫              0              t                        ⁢                                                  ⁢                                          ⅆ                                  t                  ′                                            ⁢                              V                ⁡                                  (                                      t                    ′                                    )                                                                                        (        1        )            in which e is the charge of the electron and h is Planck's constant. The phase and the current I are interconnected by the inductance L, φ=2π/φ0LI, in which φ0 is the basic unit of the magnetic flux, and hence measurement of the phase expresses the direction of the current/i.e. the state of the quantum bit.
A second superconducting quantum bit is a charge-quantum bit, for which ECP≈EJ.
A tunnel junction on nanoscale may have sufficient Cooper pair charge energy in order to meet this condition. The states |0> and |1> of the charge-quantum bit correspond to the fact whether the superconductor island defined by one or more tunnel junctions has zero or one Cooper pair relative to a charge neutral situation. For measurement of the state of a charge-quantum bit, a sensitive electric charge measurement instrument is needed, i.e. an electrometer, such as rf-SET or L-SET.
The charge-phase quantum bit is perhaps the most interesting superconducting quantum bit. As in the case of a charge-quantum bit, the computing operations of a quantum bit are performed by charge signals. Measurement, again, is performed in principle in the same way as for a phase-quantum bit, i.e. by measuring the phase over the quantum bit, because the states |0> and |1> involve different phases. For the measurement, the quantum bit in the original application is short-circuited by a superconducting loop having one large-sized tunnel junction. The measurement has been performed by conducting a current pulse to the structure. Depending on the state of the quantum bit, the current of the large-sized tunnel junction either exceeds or does not exceed a critical value, so that a voltage is or is not generated over the structure. This voltage is the final variable indicating the state of the charge-phase quantum bit in the measurement method of the original solution.
The operation of all of the quantum bits mentioned above have been experimentally proved as individual elements of quantum logics. One has recently even managed to interconnect two charge-quantum bits, thus achieving a very elementary quantum computer processor.